Ultimately, a warm-up is just that: an exercise to re-acquaint the player with their instrument and warm up the parts of the Self which need it. Since the Self includes both mind and body, a warm-up should be done with calm, balanced attention.
However, many people, including myself at times, warm-up in a way which may not be useful, and may even be detrimental to overall playing.
A nervous, loud, fast scale, played without thinking, will do little to engage the fine motor muscles needed to play long controlled phrases, or pianissimo held notes. Nor will it help to re-acquaint the player with the subtle poise necessary to play fast, complex technical passages.
Perhaps the player has learned a well researched and trusted warm-up from a teacher. But if he or she rushes through it to "get to the good stuff", the purpose of the warm up becomes moot.
Over time and many repetitions, any habitual warm-up practice can easily become tainted by mis-use if it is not performed with calm and detailed attention.
Some questions to ask yourself as you warm up:
1) Are you "in the room", present and accounted for both physically and mentally?
2) Have you adjusted your posture and Use to be efficient and productive; neck free, back long and wide, hips free, feet flat on ground, shoulders floating on rib cage, jaw relaxed, eyes relaxed?
3) Does your warm up cover several basic techniques, such as (for wind players) air, embouchure muscles, and finger motions?
4) How does today's warm up compare to yesterday or the general trend? It is important to measure the relative health of your overall technique from day to day via your warm up. Feedback from your self may indicate whether you are mis-using or overdoing something during practice or performance, and may need a longer warm-up on some days.
The best players have learned to use themselves so well that they barely need to play the instrument before being able to execute advanced techniques. In other words, the ultimate goal is to need little or no warm up, and to carry yourself through out the day in such a way as to always be ready to play. This is done through awareness and memory of how it feels to play. The better you memorize a healthy, warmed up feeling, the more in tune you are to your instrument, and your Self, at all times.